The most commonly used data structure to implement a breadth-first search (BFS) algorithm is a queue. In a BFS, we explore the nodes of a graph or tree in a breadthward motion, i.e., we first explore all the nodes at the same level before moving to a deeper level.

  The queue data structure follows a First-In-First-Out (FIFO) ordering principle, which is ideal for a BFS traversal. The idea is to enqueue the starting node or nodes (if multiple starting nodes) into the queue and then repeatedly dequeue a node, visit its adjacent unvisited nodes, and enqueue them into the queue. This process continues until the queue becomes empty or the desired condition is met.

  By using a queue, the BFS algorithm ensures that nodes are visited in the order of their distance from the starting node. This guarantees that the algorithm explores all the nodes at the same level before moving to deeper levels. Without the use of a queue, we would not maintain the correct order of visiting nodes.

  Additionally, to keep track of visited nodes and avoid revisiting them, we usually use a separate data structure such as a set or an array. This helps improve the efficiency of the BFS algorithm by preventing unnecessary reprocessing of nodes.

  In summary, a queue is the typical data structure used to implement a breadth-first search algorithm as it provides the necessary ordering for exploring nodes at the same level before moving deeper, allowing for a systematic traversal of a graph or tree.